In the prior application U.S. application Ser. No. 12/895,408, pulses are transmitted into a scene by an array of transducers. A pattern of wideband ultrasound frequencies in each pulse is unique with respect to the patterns of each other pulse. Received signals are sampled and decomposed using a Fourier transform to produce frequency coefficients, which are stacked to produce a linear system modeling a reflectivity of the scene, which is reconstructed as an image. The principles in the signal acquisition described therein are similar as for the present application, however the reconstruction methodology is not.
In the prior application Ser. No. 13/721,350, a scene is also reconstructed by receiving reflected signals due to pulses transmitted by a virtual array of transducers. The virtual array has a set of configurations subject to positioning errors. The received signal are sampled and decomposed to produce frequency coefficients stacked in a set of linear systems modeling a reflectivity of the scene. There is one linear system for each array configuration. A reconstruction method is applied to the set of linear systems. The reconstruction method solves each linear system separately to obtain a corresponding solution. The corresponding solutions share information during the solving, and the solutions are combined to reconstruct the scene.
One issue with the prior applications is the accuracy the array positioning. An ultrasonic array operating at 50 kHz has a wavelength of approximately 6.88 mm, which means that element positioning needs be accurate to less than a millimeter. Such tolerances are difficult to manufacture, especially in a mass-produced system. Another issue is the computational complexity of the reconstruction process, particularly when convex optimization or greedy methods are used in and embedded system with limited resources.
It is desired to improve on the reconstruction used in the related applications.